Finite Group Databasebeta

← Group #11798894

Character table — Group #11798894

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57
size11112244444444448888888888881818181818182424242436363636363636363648484848484848484848
order122244336666668812121212242424242424242444888844444161616161616161622666612121212
χ1111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ31111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1111111-1-1-1-1
χ511111111111111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-11111-1-1-1-11-111-1-1-1-111
χ611111111111111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-11111-11-1-111-1-111
χ711111111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-11111-1-1-1-1-11-1-11111-1-1
χ811111111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-111111-111-1-111-1-1
χ92222222222222222222222222222-2-2-2-2-2-20000-2000000000000000000
χ1022222222222222-2-22222-2-2-2-2-2-2-2-222-2-2-2-200002000000000000000000
χ112222-2-22222222200-2-2-2-2000000002200000000-222−2−222−2−20000000000
χ122222-2-22222222200-2-2-2-2000000002200000000-2−2−222−2−2220000000000
χ132222-2-22222222200-2-2-2-200000000-2-200000000222−2−2−2−2220000000000
χ142222-2-22222222200-2-2-2-200000000-2-2000000002−2−22222−2−20000000000
χ1522-2-2002222-2-2-2-22−200002222−2−2−2−22-22−22−200000−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ430000000000
χ1622-2-2002222-2-2-2-22−200002222−2−2−2−22-22−22−200000ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ430000000000
χ1722-2-2002222-2-2-2-22−200002222−2−2−2−2-22−22−2200000ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ470000000000
χ1822-2-2002222-2-2-2-22−200002222−2−2−2−2-22−22−2200000−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ470000000000
χ1922-2-2002222-2-2-2-2−220000−2−2−2−222222-2−22−2200000ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ470000000000
χ2022-2-2002222-2-2-2-2−220000−2−2−2−222222-2−22−2200000−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ470000000000
χ2122-2-2002222-2-2-2-2−220000−2−2−2−22222-222−22−200000−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ430000000000
χ2222-2-2002222-2-2-2-2−220000−2−2−2−22222-222−22−200000ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ430000000000
χ232-22-2-2222-2-2-22-220022-2-2000000000022-2-2002i−2i0000000000000002i−2i00
χ242-22-2-2222-2-2-22-220022-2-2000000000022-2-200−2i2i000000000000000−2i2i00
χ252-22-2-2222-2-2-22-220022-2-20000000000-2-2222-200000000000000000002-2
χ262-22-2-2222-2-2-22-220022-2-20000000000-2-222-220000000000000000000-22
χ274444441-21-2-2-21144-21-2111-2-211-2-20000002222000000000000000-1-1-1-1
χ284444441-21-2-2-21144-21-2111-2-211-2-2000000-2-2-2-20000000000000001111
χ294444441-21-2-2-211-4-4-21-21-1-122-1-12200000022-2-200000000000000011-1-1
χ304444441-21-2-2-211-4-4-21-21-1-122-1-122000000-2-222000000000000000-1-111
χ31444444-21-2111-2-2441-21-2-2-211-2-211000000000000000000022-1-1-1-10000
χ32444444-21-2111-2-2441-21-2-2-211-2-2110000000000000000000-2-211110000
χ33444444-21-2111-2-2-4-41-21-222-1-122-1-100000000000000000002-2-1-1110000
χ34444444-21-2111-2-2-4-41-21-222-1-122-1-10000000000000000000-2211-1-10000
χ354-44-44-444-4-4-44-4400-4-4440000000000000000000000000000000000000
χ364-44-44-4-212-1-112-200-121-2003-3003-3000000000000000000000−i3i3−i3i30000
χ374-44-44-4-212-1-112-200-121-2003-3003-3000000000000000000000i3−i3i3−i30000
χ384-44-44-4-212-1-112-200-121-200-3300-33000000000000000000000−i3i3i3−i30000
χ394-44-44-4-212-1-112-200-121-200-3300-33000000000000000000000i3−i3−i3i30000
χ404-44-4-441-2-122-2-1100-212-13i−3i003i−3i000000002-22i−2i000000000000000−ii-11
χ414-44-4-441-2-122-2-1100-212-13i−3i003i−3i00000000-22−2i2i000000000000000i−i1-1
χ424-44-4-441-2-122-2-1100-212-1−3i3i00−3i3i000000002-2−2i2i000000000000000i−i-11
χ434-44-4-441-2-122-2-1100-212-1−3i3i00−3i3i00000000-222i−2i000000000000000−ii1-1
χ444-4-440044-4-44-44-4000000000000000022−22−222200000000000000000000000
χ454-4-440044-4-44-44-40000000000000000−222222−2200000000000000000000000
χ468888-8-82-42-4-4-422004-24-20000000000000000000000000000000000000
χ478888-8-8-42-4222-4-400-24-240000000000000000000000000000000000000
χ4888-8-8002-42-444-2-242−42000022−22−22−2−2222200000000000000000000000000000
χ4988-8-8002-42-444-2-2−42420000−2−2222222−22−2200000000000000000000000000000
χ5088-8-800-42-42-2-24442−420000−22−22222222−2−200000000000000000000000000000
χ5188-8-800-42-42-2-244−424200002222−2−2−22−222200000000000000000000000000000
χ528-88-88-82-4-244-4-22004-2-420000000000000000000000000000000000000
χ538-88-8-88-424-2-224-4002-4-240000000000000000000000000000000000000
χ548-8-88002-4-24-442-2000000−3i23i2003i2−3i20000000000000000000000000000000
χ558-8-88002-4-24-442-20000003i2−3i200−3i23i20000000000000000000000000000000
χ568-8-8800-424-22-2-440000000032−3200−323200000000000000000000000000000
χ578-8-8800-424-22-2-4400000000−32320032−3200000000000000000000000000000

Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.